Highest Common Factor of 807, 946, 916 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 807, 946, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 807, 946, 916 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 807, 946, 916 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 807, 946, 916 is 1.

HCF(807, 946, 916) = 1

HCF of 807, 946, 916 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 807, 946, 916 is 1.

Highest Common Factor of 807,946,916 using Euclid's algorithm

Highest Common Factor of 807,946,916 is 1

Step 1: Since 946 > 807, we apply the division lemma to 946 and 807, to get

946 = 807 x 1 + 139

Step 2: Since the reminder 807 ≠ 0, we apply division lemma to 139 and 807, to get

807 = 139 x 5 + 112

Step 3: We consider the new divisor 139 and the new remainder 112, and apply the division lemma to get

139 = 112 x 1 + 27

We consider the new divisor 112 and the new remainder 27,and apply the division lemma to get

112 = 27 x 4 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 807 and 946 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(112,27) = HCF(139,112) = HCF(807,139) = HCF(946,807) .

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

Step 1: Since 916 > 1, we apply the division lemma to 916 and 1, to get

916 = 1 x 916 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 916 is 1

Notice that 1 = HCF(916,1) .

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Frequently Asked Questions on HCF of 807, 946, 916 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 807, 946, 916?

Answer: HCF of 807, 946, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 807, 946, 916 using Euclid's Algorithm?

Answer: For arbitrary numbers 807, 946, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.