Highest Common Factor of 969, 700, 410 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 969, 700, 410 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 969, 700, 410 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 969, 700, 410 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 969, 700, 410 is 1.

HCF(969, 700, 410) = 1

HCF of 969, 700, 410 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 969, 700, 410 is 1.

Highest Common Factor of 969,700,410 using Euclid's algorithm

Highest Common Factor of 969,700,410 is 1

Step 1: Since 969 > 700, we apply the division lemma to 969 and 700, to get

969 = 700 x 1 + 269

Step 2: Since the reminder 700 ≠ 0, we apply division lemma to 269 and 700, to get

700 = 269 x 2 + 162

Step 3: We consider the new divisor 269 and the new remainder 162, and apply the division lemma to get

269 = 162 x 1 + 107

We consider the new divisor 162 and the new remainder 107,and apply the division lemma to get

162 = 107 x 1 + 55

We consider the new divisor 107 and the new remainder 55,and apply the division lemma to get

107 = 55 x 1 + 52

We consider the new divisor 55 and the new remainder 52,and apply the division lemma to get

55 = 52 x 1 + 3

We consider the new divisor 52 and the new remainder 3,and apply the division lemma to get

52 = 3 x 17 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 969 and 700 is 1

Notice that 1 = HCF(3,1) = HCF(52,3) = HCF(55,52) = HCF(107,55) = HCF(162,107) = HCF(269,162) = HCF(700,269) = HCF(969,700) .

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

Step 1: Since 410 > 1, we apply the division lemma to 410 and 1, to get

410 = 1 x 410 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 410 is 1

Notice that 1 = HCF(410,1) .

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Frequently Asked Questions on HCF of 969, 700, 410 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 969, 700, 410?

Answer: HCF of 969, 700, 410 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 969, 700, 410 using Euclid's Algorithm?

Answer: For arbitrary numbers 969, 700, 410 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.