Highest Common Factor of 120, 975 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 120, 975 i.e. 15 the largest integer that leaves a remainder zero for all numbers.

HCF of 120, 975 is 15 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 120, 975 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 120, 975 is 15.

HCF(120, 975) = 15

HCF of 120, 975 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 120, 975 is 15.

Highest Common Factor of 120,975 using Euclid's algorithm

Highest Common Factor of 120,975 is 15

Step 1: Since 975 > 120, we apply the division lemma to 975 and 120, to get

975 = 120 x 8 + 15

Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 15 and 120, to get

120 = 15 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 120 and 975 is 15

Notice that 15 = HCF(120,15) = HCF(975,120) .

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Frequently Asked Questions on HCF of 120, 975 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 120, 975?

Answer: HCF of 120, 975 is 15 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 120, 975 using Euclid's Algorithm?

Answer: For arbitrary numbers 120, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.