Highest Common Factor of 972, 702, 105 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, 702, 105 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 702, 105 is 3 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, 702, 105 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, 702, 105 is 3.

HCF(972, 702, 105) = 3

HCF of 972, 702, 105 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 972, 702, 105 is 3.

Highest Common Factor of 972,702,105 using Euclid's algorithm

Highest Common Factor of 972,702,105 is 3

Step 1: Since 972 > 702, we apply the division lemma to 972 and 702, to get

972 = 702 x 1 + 270

Step 2: Since the reminder 702 ≠ 0, we apply division lemma to 270 and 702, to get

702 = 270 x 2 + 162

Step 3: We consider the new divisor 270 and the new remainder 162, and apply the division lemma to get

270 = 162 x 1 + 108

We consider the new divisor 162 and the new remainder 108,and apply the division lemma to get

162 = 108 x 1 + 54

We consider the new divisor 108 and the new remainder 54,and apply the division lemma to get

108 = 54 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 972 and 702 is 54

Notice that 54 = HCF(108,54) = HCF(162,108) = HCF(270,162) = HCF(702,270) = HCF(972,702) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 105 > 54, we apply the division lemma to 105 and 54, to get

105 = 54 x 1 + 51

Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 51 and 54, to get

54 = 51 x 1 + 3

Step 3: We consider the new divisor 51 and the new remainder 3, and apply the division lemma to get

51 = 3 x 17 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 54 and 105 is 3

Notice that 3 = HCF(51,3) = HCF(54,51) = HCF(105,54) .

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Frequently Asked Questions on HCF of 972, 702, 105 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, 702, 105?

Answer: HCF of 972, 702, 105 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 702, 105 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 702, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.