Highest Common Factor of 22, 55, 78, 157 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 22, 55, 78, 157 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 22, 55, 78, 157 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 22, 55, 78, 157 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 22, 55, 78, 157 is 1.
HCF(22, 55, 78, 157) = 1
HCF of 22, 55, 78, 157 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 22, 55, 78, 157 is 1.
Highest Common Factor of 22,55,78,157 is 1
Step 1: Since 55 > 22, we apply the division lemma to 55 and 22, to get
55 = 22 x 2 + 11
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 11 and 22, to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 22 and 55 is 11
Notice that 11 = HCF(22,11) = HCF(55,22) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 11, we apply the division lemma to 78 and 11, to get
78 = 11 x 7 + 1
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 1 and 11, to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 78 is 1
Notice that 1 = HCF(11,1) = HCF(78,11) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 157 > 1, we apply the division lemma to 157 and 1, to get
157 = 1 x 157 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 157 is 1
Notice that 1 = HCF(157,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 22, 55, 78, 157 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 22, 55, 78, 157?
Answer: HCF of 22, 55, 78, 157 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 22, 55, 78, 157 using Euclid's Algorithm?
Answer: For arbitrary numbers 22, 55, 78, 157 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.