Highest Common Factor of 762, 907, 688 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 762, 907, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 762, 907, 688 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 762, 907, 688 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 762, 907, 688 is 1.

HCF(762, 907, 688) = 1

HCF of 762, 907, 688 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 762, 907, 688 is 1.

Highest Common Factor of 762,907,688 using Euclid's algorithm

Highest Common Factor of 762,907,688 is 1

Step 1: Since 907 > 762, we apply the division lemma to 907 and 762, to get

907 = 762 x 1 + 145

Step 2: Since the reminder 762 ≠ 0, we apply division lemma to 145 and 762, to get

762 = 145 x 5 + 37

Step 3: We consider the new divisor 145 and the new remainder 37, and apply the division lemma to get

145 = 37 x 3 + 34

We consider the new divisor 37 and the new remainder 34,and apply the division lemma to get

37 = 34 x 1 + 3

We consider the new divisor 34 and the new remainder 3,and apply the division lemma to get

34 = 3 x 11 + 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 762 and 907 is 1

Notice that 1 = HCF(3,1) = HCF(34,3) = HCF(37,34) = HCF(145,37) = HCF(762,145) = HCF(907,762) .

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

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

688 = 1 x 688 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 688 is 1

Notice that 1 = HCF(688,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 762, 907, 688 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 762, 907, 688?

Answer: HCF of 762, 907, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 762, 907, 688 using Euclid's Algorithm?

Answer: For arbitrary numbers 762, 907, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.