Highest Common Factor of 88, 77, 15, 112 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 88, 77, 15, 112 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 88, 77, 15, 112 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 88, 77, 15, 112 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 88, 77, 15, 112 is 1.

HCF(88, 77, 15, 112) = 1

HCF of 88, 77, 15, 112 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 88, 77, 15, 112 is 1.

Highest Common Factor of 88,77,15,112 using Euclid's algorithm

Highest Common Factor of 88,77,15,112 is 1

Step 1: Since 88 > 77, we apply the division lemma to 88 and 77, to get

88 = 77 x 1 + 11

Step 2: Since the reminder 77 ≠ 0, we apply division lemma to 11 and 77, to get

77 = 11 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 88 and 77 is 11

Notice that 11 = HCF(77,11) = HCF(88,77) .


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

Step 1: Since 15 > 11, we apply the division lemma to 15 and 11, to get

15 = 11 x 1 + 4

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 4 and 11, to get

11 = 4 x 2 + 3

Step 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 11 and 15 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) .


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

Step 1: Since 112 > 1, we apply the division lemma to 112 and 1, to get

112 = 1 x 112 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 112 is 1

Notice that 1 = HCF(112,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 88, 77, 15, 112 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 88, 77, 15, 112?

Answer: HCF of 88, 77, 15, 112 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 88, 77, 15, 112 using Euclid's Algorithm?

Answer: For arbitrary numbers 88, 77, 15, 112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.