Highest Common Factor of 972, 688, 508 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, 688, 508 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 688, 508 is 4 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, 688, 508 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, 688, 508 is 4.
HCF(972, 688, 508) = 4
HCF of 972, 688, 508 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, 688, 508 is 4.
Highest Common Factor of 972,688,508 is 4
Step 1: Since 972 > 688, we apply the division lemma to 972 and 688, to get
972 = 688 x 1 + 284
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 284 and 688, to get
688 = 284 x 2 + 120
Step 3: We consider the new divisor 284 and the new remainder 120, and apply the division lemma to get
284 = 120 x 2 + 44
We consider the new divisor 120 and the new remainder 44,and apply the division lemma to get
120 = 44 x 2 + 32
We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get
44 = 32 x 1 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 972 and 688 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(120,44) = HCF(284,120) = HCF(688,284) = HCF(972,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 508 > 4, we apply the division lemma to 508 and 4, to get
508 = 4 x 127 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 508 is 4
Notice that 4 = HCF(508,4) .
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Frequently Asked Questions on HCF of 972, 688, 508 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, 688, 508?
Answer: HCF of 972, 688, 508 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 688, 508 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 688, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.