Highest Common Factor of 972, 684 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, 684 i.e. 36 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 684 is 36 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, 684 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, 684 is 36.
HCF(972, 684) = 36
HCF of 972, 684 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, 684 is 36.
Highest Common Factor of 972,684 is 36
Step 1: Since 972 > 684, we apply the division lemma to 972 and 684, to get
972 = 684 x 1 + 288
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 288 and 684, to get
684 = 288 x 2 + 108
Step 3: We consider the new divisor 288 and the new remainder 108, and apply the division lemma to get
288 = 108 x 2 + 72
We consider the new divisor 108 and the new remainder 72,and apply the division lemma to get
108 = 72 x 1 + 36
We consider the new divisor 72 and the new remainder 36,and apply the division lemma to get
72 = 36 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 972 and 684 is 36
Notice that 36 = HCF(72,36) = HCF(108,72) = HCF(288,108) = HCF(684,288) = HCF(972,684) .
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Frequently Asked Questions on HCF of 972, 684 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, 684?
Answer: HCF of 972, 684 is 36 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.