Highest Common Factor of 964, 972, 639, 109 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 964, 972, 639, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 964, 972, 639, 109 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 964, 972, 639, 109 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 964, 972, 639, 109 is 1.
HCF(964, 972, 639, 109) = 1
HCF of 964, 972, 639, 109 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 964, 972, 639, 109 is 1.
Highest Common Factor of 964,972,639,109 is 1
Step 1: Since 972 > 964, we apply the division lemma to 972 and 964, to get
972 = 964 x 1 + 8
Step 2: Since the reminder 964 ≠ 0, we apply division lemma to 8 and 964, to get
964 = 8 x 120 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 964 and 972 is 4
Notice that 4 = HCF(8,4) = HCF(964,8) = HCF(972,964) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 639 > 4, we apply the division lemma to 639 and 4, to get
639 = 4 x 159 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: 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 4 and 639 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(639,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 1, we apply the division lemma to 109 and 1, to get
109 = 1 x 109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 109 is 1
Notice that 1 = HCF(109,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 964, 972, 639, 109 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 964, 972, 639, 109?
Answer: HCF of 964, 972, 639, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 964, 972, 639, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 964, 972, 639, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.