Highest Common Factor of 956, 688, 409 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 956, 688, 409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 956, 688, 409 is 1 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 956, 688, 409 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 956, 688, 409 is 1.

HCF(956, 688, 409) = 1

HCF of 956, 688, 409 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 956, 688, 409 is 1.

Highest Common Factor of 956,688,409 using Euclid's algorithm

Highest Common Factor of 956,688,409 is 1

Step 1: Since 956 > 688, we apply the division lemma to 956 and 688, to get

956 = 688 x 1 + 268

Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 268 and 688, to get

688 = 268 x 2 + 152

Step 3: We consider the new divisor 268 and the new remainder 152, and apply the division lemma to get

268 = 152 x 1 + 116

We consider the new divisor 152 and the new remainder 116,and apply the division lemma to get

152 = 116 x 1 + 36

We consider the new divisor 116 and the new remainder 36,and apply the division lemma to get

116 = 36 x 3 + 8

We consider the new divisor 36 and the new remainder 8,and apply the division lemma to get

36 = 8 x 4 + 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 956 and 688 is 4

Notice that 4 = HCF(8,4) = HCF(36,8) = HCF(116,36) = HCF(152,116) = HCF(268,152) = HCF(688,268) = HCF(956,688) .

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

Step 1: Since 409 > 4, we apply the division lemma to 409 and 4, to get

409 = 4 x 102 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 409 is 1

Notice that 1 = HCF(4,1) = HCF(409,4) .

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Frequently Asked Questions on HCF of 956, 688, 409 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 956, 688, 409?

Answer: HCF of 956, 688, 409 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 956, 688, 409 using Euclid's Algorithm?

Answer: For arbitrary numbers 956, 688, 409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.