Highest Common Factor of 975, 630, 866, 655 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 975, 630, 866, 655 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 975, 630, 866, 655 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 975, 630, 866, 655 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 975, 630, 866, 655 is 1.
HCF(975, 630, 866, 655) = 1
HCF of 975, 630, 866, 655 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 975, 630, 866, 655 is 1.
Highest Common Factor of 975,630,866,655 is 1
Step 1: Since 975 > 630, we apply the division lemma to 975 and 630, to get
975 = 630 x 1 + 345
Step 2: Since the reminder 630 ≠ 0, we apply division lemma to 345 and 630, to get
630 = 345 x 1 + 285
Step 3: We consider the new divisor 345 and the new remainder 285, and apply the division lemma to get
345 = 285 x 1 + 60
We consider the new divisor 285 and the new remainder 60,and apply the division lemma to get
285 = 60 x 4 + 45
We consider the new divisor 60 and the new remainder 45,and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 975 and 630 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(285,60) = HCF(345,285) = HCF(630,345) = HCF(975,630) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 866 > 15, we apply the division lemma to 866 and 15, to get
866 = 15 x 57 + 11
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 11 and 15, to get
15 = 11 x 1 + 4
Step 3: We consider the new divisor 11 and the new remainder 4, and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 866 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(866,15) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 655 > 1, we apply the division lemma to 655 and 1, to get
655 = 1 x 655 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 655 is 1
Notice that 1 = HCF(655,1) .
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Frequently Asked Questions on HCF of 975, 630, 866, 655 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 975, 630, 866, 655?
Answer: HCF of 975, 630, 866, 655 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 975, 630, 866, 655 using Euclid's Algorithm?
Answer: For arbitrary numbers 975, 630, 866, 655 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.