Highest Common Factor of 560, 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 560, 105 i.e. 35 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 105 is 35 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 560, 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 560, 105 is 35.

HCF(560, 105) = 35

HCF of 560, 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 560, 105 is 35.

Highest Common Factor of 560,105 using Euclid's algorithm

Highest Common Factor of 560,105 is 35

Step 1: Since 560 > 105, we apply the division lemma to 560 and 105, to get

560 = 105 x 5 + 35

Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 35 and 105, to get

105 = 35 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 560 and 105 is 35

Notice that 35 = HCF(105,35) = HCF(560,105) .

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Frequently Asked Questions on HCF of 560, 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 560, 105?

Answer: HCF of 560, 105 is 35 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 105 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.