Highest Common Factor of 972, 761, 416, 984 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 972, 761, 416, 984 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 761, 416, 984 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 972, 761, 416, 984 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 972, 761, 416, 984 is 1.
HCF(972, 761, 416, 984) = 1
HCF of 972, 761, 416, 984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 761, 416, 984 is 1.
Highest Common Factor of 972,761,416,984 is 1
Step 1: Since 972 > 761, we apply the division lemma to 972 and 761, to get
972 = 761 x 1 + 211
Step 2: Since the reminder 761 ≠ 0, we apply division lemma to 211 and 761, to get
761 = 211 x 3 + 128
Step 3: We consider the new divisor 211 and the new remainder 128, and apply the division lemma to get
211 = 128 x 1 + 83
We consider the new divisor 128 and the new remainder 83,and apply the division lemma to get
128 = 83 x 1 + 45
We consider the new divisor 83 and the new remainder 45,and apply the division lemma to get
83 = 45 x 1 + 38
We consider the new divisor 45 and the new remainder 38,and apply the division lemma to get
45 = 38 x 1 + 7
We consider the new divisor 38 and the new remainder 7,and apply the division lemma to get
38 = 7 x 5 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 972 and 761 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(38,7) = HCF(45,38) = HCF(83,45) = HCF(128,83) = HCF(211,128) = HCF(761,211) = HCF(972,761) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 416 > 1, we apply the division lemma to 416 and 1, to get
416 = 1 x 416 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 416 is 1
Notice that 1 = HCF(416,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 984 > 1, we apply the division lemma to 984 and 1, to get
984 = 1 x 984 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 984 is 1
Notice that 1 = HCF(984,1) .
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Frequently Asked Questions on HCF of 972, 761, 416, 984 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 972, 761, 416, 984?
Answer: HCF of 972, 761, 416, 984 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 761, 416, 984 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 761, 416, 984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.