Highest Common Factor of 825, 970 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 825, 970 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 825, 970 is 5 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 825, 970 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 825, 970 is 5.

HCF(825, 970) = 5

HCF of 825, 970 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 825, 970 is 5.

Highest Common Factor of 825,970 using Euclid's algorithm

Highest Common Factor of 825,970 is 5

Step 1: Since 970 > 825, we apply the division lemma to 970 and 825, to get

970 = 825 x 1 + 145

Step 2: Since the reminder 825 ≠ 0, we apply division lemma to 145 and 825, to get

825 = 145 x 5 + 100

Step 3: We consider the new divisor 145 and the new remainder 100, and apply the division lemma to get

145 = 100 x 1 + 45

We consider the new divisor 100 and the new remainder 45,and apply the division lemma to get

100 = 45 x 2 + 10

We consider the new divisor 45 and the new remainder 10,and apply the division lemma to get

45 = 10 x 4 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 825 and 970 is 5

Notice that 5 = HCF(10,5) = HCF(45,10) = HCF(100,45) = HCF(145,100) = HCF(825,145) = HCF(970,825) .

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Frequently Asked Questions on HCF of 825, 970 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 825, 970?

Answer: HCF of 825, 970 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 825, 970 using Euclid's Algorithm?

Answer: For arbitrary numbers 825, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.