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 220, 337, 645, 975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 220, 337, 645, 975 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 220, 337, 645, 975 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 220, 337, 645, 975 is 1.
HCF(220, 337, 645, 975) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 220, 337, 645, 975 is 1.
Step 1: Since 337 > 220, we apply the division lemma to 337 and 220, to get
337 = 220 x 1 + 117
Step 2: Since the reminder 220 ≠ 0, we apply division lemma to 117 and 220, to get
220 = 117 x 1 + 103
Step 3: We consider the new divisor 117 and the new remainder 103, and apply the division lemma to get
117 = 103 x 1 + 14
We consider the new divisor 103 and the new remainder 14,and apply the division lemma to get
103 = 14 x 7 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 220 and 337 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(103,14) = HCF(117,103) = HCF(220,117) = HCF(337,220) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 645 > 1, we apply the division lemma to 645 and 1, to get
645 = 1 x 645 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 645 is 1
Notice that 1 = HCF(645,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 975 > 1, we apply the division lemma to 975 and 1, to get
975 = 1 x 975 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 975 is 1
Notice that 1 = HCF(975,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 220, 337, 645, 975?
Answer: HCF of 220, 337, 645, 975 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 220, 337, 645, 975 using Euclid's Algorithm?
Answer: For arbitrary numbers 220, 337, 645, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.