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 157, 762, 501, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 157, 762, 501, 77 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 157, 762, 501, 77 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 157, 762, 501, 77 is 1.
HCF(157, 762, 501, 77) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 157, 762, 501, 77 is 1.
Step 1: Since 762 > 157, we apply the division lemma to 762 and 157, to get
762 = 157 x 4 + 134
Step 2: Since the reminder 157 ≠ 0, we apply division lemma to 134 and 157, to get
157 = 134 x 1 + 23
Step 3: We consider the new divisor 134 and the new remainder 23, and apply the division lemma to get
134 = 23 x 5 + 19
We consider the new divisor 23 and the new remainder 19,and apply the division lemma to get
23 = 19 x 1 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 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 157 and 762 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(23,19) = HCF(134,23) = HCF(157,134) = HCF(762,157) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 501 > 1, we apply the division lemma to 501 and 1, to get
501 = 1 x 501 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 501 is 1
Notice that 1 = HCF(501,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get
77 = 1 x 77 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1
Notice that 1 = HCF(77,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 157, 762, 501, 77?
Answer: HCF of 157, 762, 501, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 157, 762, 501, 77 using Euclid's Algorithm?
Answer: For arbitrary numbers 157, 762, 501, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.