Highest Common Factor of 369, 972 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 369, 972 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 369, 972 is 9 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 369, 972 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 369, 972 is 9.
HCF(369, 972) = 9
HCF of 369, 972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 369, 972 is 9.
Highest Common Factor of 369,972 is 9
Step 1: Since 972 > 369, we apply the division lemma to 972 and 369, to get
972 = 369 x 2 + 234
Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 234 and 369, to get
369 = 234 x 1 + 135
Step 3: We consider the new divisor 234 and the new remainder 135, and apply the division lemma to get
234 = 135 x 1 + 99
We consider the new divisor 135 and the new remainder 99,and apply the division lemma to get
135 = 99 x 1 + 36
We consider the new divisor 99 and the new remainder 36,and apply the division lemma to get
99 = 36 x 2 + 27
We consider the new divisor 36 and the new remainder 27,and apply the division lemma to get
36 = 27 x 1 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 369 and 972 is 9
Notice that 9 = HCF(27,9) = HCF(36,27) = HCF(99,36) = HCF(135,99) = HCF(234,135) = HCF(369,234) = HCF(972,369) .
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Frequently Asked Questions on HCF of 369, 972 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 369, 972?
Answer: HCF of 369, 972 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 369, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 369, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.