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 961, 5356, 7565 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 961, 5356, 7565 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 961, 5356, 7565 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 961, 5356, 7565 is 1.
HCF(961, 5356, 7565) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 961, 5356, 7565 is 1.
Step 1: Since 5356 > 961, we apply the division lemma to 5356 and 961, to get
5356 = 961 x 5 + 551
Step 2: Since the reminder 961 ≠ 0, we apply division lemma to 551 and 961, to get
961 = 551 x 1 + 410
Step 3: We consider the new divisor 551 and the new remainder 410, and apply the division lemma to get
551 = 410 x 1 + 141
We consider the new divisor 410 and the new remainder 141,and apply the division lemma to get
410 = 141 x 2 + 128
We consider the new divisor 141 and the new remainder 128,and apply the division lemma to get
141 = 128 x 1 + 13
We consider the new divisor 128 and the new remainder 13,and apply the division lemma to get
128 = 13 x 9 + 11
We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get
13 = 11 x 1 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 961 and 5356 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(128,13) = HCF(141,128) = HCF(410,141) = HCF(551,410) = HCF(961,551) = HCF(5356,961) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7565 > 1, we apply the division lemma to 7565 and 1, to get
7565 = 1 x 7565 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7565 is 1
Notice that 1 = HCF(7565,1) .
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 961, 5356, 7565?
Answer: HCF of 961, 5356, 7565 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 961, 5356, 7565 using Euclid's Algorithm?
Answer: For arbitrary numbers 961, 5356, 7565 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.