Highest Common Factor of 264, 462, 962 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 264, 462, 962 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 264, 462, 962 is 2 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 264, 462, 962 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 264, 462, 962 is 2.
HCF(264, 462, 962) = 2
HCF of 264, 462, 962 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 264, 462, 962 is 2.
Highest Common Factor of 264,462,962 is 2
Step 1: Since 462 > 264, we apply the division lemma to 462 and 264, to get
462 = 264 x 1 + 198
Step 2: Since the reminder 264 ≠ 0, we apply division lemma to 198 and 264, to get
264 = 198 x 1 + 66
Step 3: We consider the new divisor 198 and the new remainder 66, and apply the division lemma to get
198 = 66 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 66, the HCF of 264 and 462 is 66
Notice that 66 = HCF(198,66) = HCF(264,198) = HCF(462,264) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 962 > 66, we apply the division lemma to 962 and 66, to get
962 = 66 x 14 + 38
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 38 and 66, to get
66 = 38 x 1 + 28
Step 3: We consider the new divisor 38 and the new remainder 28, and apply the division lemma to get
38 = 28 x 1 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 66 and 962 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(66,38) = HCF(962,66) .
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Frequently Asked Questions on HCF of 264, 462, 962 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 264, 462, 962?
Answer: HCF of 264, 462, 962 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 264, 462, 962 using Euclid's Algorithm?
Answer: For arbitrary numbers 264, 462, 962 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.